state the law of conservation of momentom prove it by using neton's third law of motion
Answers
Explanation:
Law of conservation of momentum states that
For two or more bodies in an isolated system acting upon each other, their total momentum remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed.
The law of conservation of momentum is an important consequence of Newton’s third law of motion.
Derivation of Conservation of Momentum
Consider two colliding particles A and B whose masses are m1 and m2 with initial and final velocities as u1 and v1 of A and u2 and v2 of B. The time of contact between two particles is given as t.
A=m1(v1−u1) (change in momentum of particle A)
B=m2(v2−u2) (change in momentum of particle B)
FBA=−FAB (from third law of motion)
FBA=m2∗a2=m2(v2−u2)t FAB=m1∗a1=m1(v1−u1)t m2(v2−u2)t=−m1(v1−u1)t m1u1+m2u2=m1v1+m2v2
Therefore, above is the equation of law of conservation of momentum where m1u1+m2u2 is the representation of total momentum of particles A and B before the collision and m1v1+m2v2 is the representation of total momentum of particles A and B after the collision.
Answer:
The Magnitude of total final momentum = The Magnitude of total initial momentum.
Explanation:
Suppose an object A has mass m1 and its initial velocity is u1.
An object B has mass m2 and its initial velocity u2.
According to formula for momentum, the initial momentum of A is m1u1 and that of B is m2u2.
Suppose these two objects collide. Let the force on A due to B be F1. This force will cause acceleration in A and its velocity will become v1.
.•. Momentum of A after collision=m1v1.
According to Newton's Third law of motion, A also exerts an equal force on B but in the opposite direction. This will cause a change in the momentum of B. If its velocity after collision is v2.
The momentum of B after collision =m2v2. If F2 is the force that acts on object B,
F2= -F1
.•. m2a2 = -m1a1...........•.• F =ma
.•. m2×(v2-u2)/t = - m1× (v1-u1)/t
.•. m2(v2-u2) = -m1(v1-u1)
.•. m2v2 - m2u2 = m1 v1 - m1u1
.•. (m2v2+m1v1) = (m2-u2+ m1u1)
hence proved